An optimal orthogonal overlay for a cyclostationary legacy signal

In this paper, the design of an overlay system is considered that operates on a channel already occupied by a legacy system. It is assumed that the legacy transmitter generates a cyclostationary signal, and that the legacy receiver is equipped with a linear filter followed by a uniform sampler. Under a zero-interference constraint at the legacy receiver, the meansquared error at the overlay receiver is minimized to find the optimal overlay system that employs linear modulation and demodulation. For the trade-off between performance and rate of the overlay system, the problem is formulated to allow a transmission rate that is a fraction of the fundamental cycle frequency of the legacy signal. The notion of a virtual legacy receiver is devised to incorporate cases with non-identical frequency bands for the transmission and reception of the overlay signal. Using the vectorized Fourier transform technique, the problem is reformulated, the solution is derived, and a necessary and sufficient condition for the existence of the optimal solution is found, all in the frequency domain. Numerical results show that the proposed scheme significantly improves the spectral efficiency by effectively exploiting the cyclostationarity of the legacy signal.